Question

Answer is (D) but how?? ​

Answer 1

$</p><p></p><p>\mathtt{Question:} </p><p></p><p>\\ \\</p><p></p><p>\quad \sec A + \tan A = x </p><p></p><p>\\ \\</p><p></p><p>\mathtt{To \; Find:} \qquad \sec A =\: ?</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad \sec A + \tan A = x </p><p></p><p>\\ \\</p><p></p><p>\mathtt{Square \; both \; sides}</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad \left( \sec A + \tan A \right)^{2} = x^{2} </p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad \sec^{2} A + \tan^{2} A + 2 \: \sec A \: \tan A = x^{2} </p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad \sec^{2} A + \sec^{2} A - 1 + 2 \: \sec A \: \tan A = x^{2} \qquad \left( \because \; 1 + \tan^{2} A = \sec^{2} A \right)</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad 2 \: \sec^{2} A + 2 \: \sec A \: \tan A = x^{2} + 1</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad 2 \: sec A \left( \sec A + \tan A \right) = x^{2} + 1</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad 2 \cdot \sec A \cdot x = x^{2} + 1 \qquad \left( \; given, \; \sec A + \tan A = x \right)</p><p></p><p>\\ \\ </p><p></p><p>\rightarrow \quad \bold{\sec A = \frac{x^{2} + 1}{2x} }</p><p></p><p>\\ \\</p><p></p><p>\qquad \bold{ Answer: \; ( D ) }</p><p></p><p>$